The annual retrograde nutation variability

International audienceVery Long Baseline Interferometry is theonly technique that can estimate Earth nutations withan accuracy under the milliarcsecond level. With 35years of geodetic VLBI observations, the principal nu-tation terms caused by luni-solar tides and geophysicalresponse have been estimated. We focus on the vari-ability. Two of them present very significant amplitudeand phase variations: the retrograde Free Core Nuta-tion (FCN) with a period of around 430 days and theAnnual Retrograde Nutation (ARN). Despite progressmade in global circulation models, the atmospheric andocean excitation cannot account for that. In particularthe ARN shows an amplitude modulation of approxi-mately six years, reminiscent of the six-year geomag-netic oscillation in the Length-of-Day (LOD). As to thelatter, we suggest that the nutation term variability mayhave deep Earth causes, and we estimate an order ofmagnitude of Earth internal structure parameters to ex-plain this variability.KeywordsNutation, least-squares adjustment, ARN1 IntroductionThe last approved nutation model, MHB2000 [14], wasderived from VLBI data. They have adjusted 1365 luni-solar and planetary terms, associating constant ampli-tudes and phases with each of them. But this modelwas unsuccessful in explaining the free core nutation(FCN) that increases by more than 100 μas at someSYRTE, Observatoire de Paris, PSL Research University, CNRS,Sorbonne Universit ́es, UPMC Univ.times. This nutation arises from a geophysical responseto luni-solar attraction, and it finds its source in the cou-pling between the fluid outer core and the mantle. Thiscoupling can be of viscous nature, of electromagneticnature, or due to the topography of the boundary.Therefore, to estimate correctly the variation ofthe FCN is important for the understanding of the in-ner structure of the Earth. Many studies have beenpublished on its estimation, and several models exist:Malkin (2013) [12], Kr ́asn ́a et al. (2013) [10], Belda etal. (2016) [1]. One of them has been selected as ref-erence by the IERS: the Lambert model1[16]). Theseworks have in common that they estimate the variabil-ity using a window with a width on the order of theFCN period. The proximity of the annual retrogradenutation (ARN) with the FCN can be dangerous be-cause of the beat phenomenon. Given the variability ofthe FCN and possibly of the ARN, a least-squares ad-justment approach may not succeed